Hydrogen is an environmentally friendly alternative to conventional fossil fuels and is considered as a renewable energy carrier for meeting the ever-increasing energy demand. Although hydrogen is abundant on earth in the form of compounds such as water, producing molecular hydrogen demands a large amount of energy. A solid oxide electrolysis cell (SOEC) is an electrochemical device which generates hydrogen from various sources. An SOEC uses high temperature (>800°C) to electrolyse water with high efficiency assisted by thermodynamically favoured water splitting that enables large-scale hydrogen production. This review provides a comprehensive overview of the current status in the developments of high-temperature steam electrolysis using a proton- and oxygen-ion-conducting SOEC system for hydrogen production. The present review summarises the detailed approaches for hydrogen production using SOECs, basic principles, challenges in designing hydrogen and oxygen electrodes and electrolytes, and potential solutions to durability issues.